Question

Which of the following order is correct for the size of \(\mathrm{Fe}^{3+}, \mathrm{Fe}\) and \(\mathrm{Fe}^{2+} ?\) (a) \(\mathrm{Fe}<\mathrm{Fe}^{2+}<\mathrm{Fe}^{3+}\) (b) \(\mathrm{Fe}^{2+}<\mathrm{Fe} 3+<\mathrm{Fe}\) (c) \(\mathrm{Fe}<\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}\) (d) \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}\)

Short answer

The correct order is (d) {Fe}^{3+} < {Fe}^{2+} < {Fe}.

Step-by-step solution

Understand the Concept

Ions of the same element can differ in size due to changes in electron configuration and repulsion. Loss of electrons leads to a decrease in radius as the remaining electrons experience a greater effective nuclear charge due to the proton-to-electron ratio increase.

Evaluate Atomic and Ionic Size

The atomic radius of neutral iron (Fe) is larger than its ions because the atomic form has more electrons, which results in more electron-electron repulsion. As electrons are removed to form cations ({Fe}^{2+} and {Fe}^{3+}), the size decreases.

Compare Ions with Different Charges

Between {Fe}^{2+} and {Fe}^{3+}, {Fe}^{3+} is smaller because it has lost more electrons and, consequently, experiences less electron-electron repulsion and a stronger effective nuclear charge.

Arrange in Order of Size

The order of size from smallest to largest is: {Fe}^{3+} < {Fe}^{2+} < {Fe}. This is because {Fe} has the most electrons and therefore the largest size, while {Fe}^{3+} has the fewest electrons and therefore the smallest size.

Key concepts

Effective Nuclear Charge

The effective nuclear charge is a crucial concept in understanding the behavior of atoms and their ions. It's basically the net positive charge experienced by an electron in an atom. For iron (Fe), each electron feels a pull from protons in the nucleus. When an atom loses electrons and becomes a cation, the remaining electrons experience a greater effective nuclear charge. This is because the electron-proton balance has shifted.

• With fewer electrons, there's less shielding from the positive pull of the nucleus.
• This stronger pull leads to a decrease in the size of the ion.

For example, in Fe^{3+} the ionic charge is increased compared to Fe^{2+}, enhancing the effective nuclear charge seen by remaining electrons. Hence, Fe^{3+} ions are smaller than both Fe^{2+} and a neutral Fe atom.

Cations

Cations are positively charged ions formed when an atom loses one or more electrons. In our example, iron can form Fe^{2+} and Fe^{3+} cations.

• When Fe loses two electrons, it forms the Fe^{2+} ion.
• Losing three electrons results in the formation of the Fe^{3+} ion.

The formation of these cations is important when determining size. Cations are generally smaller than their neutral atoms due to the loss of electron repulsion. For instance, Fe is larger than Fe^{2+} and Fe^{3+}. As more electrons are removed, the ionic radius gets even smaller.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom or ion's atomic orbitals. For neutral iron (Fe), the electron configuration is:\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\]When iron loses electrons to become a cation, this configuration changes.

• For Fe^{2+}, it loses two electrons, modifying the configuration to 1s^2 2s^2 2p^6 3s^2 3p^6 3d^6.
• For Fe^{3+}, it loses three electrons, giving it the configuration 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5.

The loss of electrons from the outermost shell decreases the electron-electron repulsion, allowing the electrons to be drawn closer to the nucleus. Thus, cations tend to be smaller than their neutral counterparts.

Atomic Radius

Atomic radius is an important property that describes the size of an atom. In general, the atomic radius decreases as we move across a period on the periodic table due to an increase in effective nuclear charge. For ions, the atomic radius can also decrease when electrons are removed to form cations.

• Neutral iron has a larger atomic radius compared to its cations because it contains more electrons, leading to increased electron repulsion.
• Fe^{2+} has lost two electrons and is thus smaller, while Fe^{3+} has lost more electrons, causing it to have the smallest atomic radius of the three.

Understanding these changes in atomic radius helps explain the sequence of sizes from Fe^{3+} < Fe^{2+} < Fe.